# Locally testable codes and PCPs of almost-linear length

@article{Goldreich2006LocallyTC, title={Locally testable codes and PCPs of almost-linear length}, author={Oded Goldreich and Madhu Sudan}, journal={Electron. Colloquium Comput. Complex.}, year={2006} }

We initiate a systematic study of locally testable codes; that is, error-correcting codes that admit very efficient membership tests. Specifically, these are codes accompanied with tests that make a constant number of (random) queries into any given word and reject non-codewords with probability proportional to their distance from the code.Locally testable codes are believed to be the combinatorial core of PCPs. However, the relation is less immediate than commonly believed. Nevertheless, we…

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